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Physica Scripta

Optical bistability and related phase transitions in an electron–hole system

G. S. Tripathi, Subrat K. Shadangi, Sukanta K. Tripathy, Sanjeev K. Nayak

Published May 27, 2026• 0 citations

Abstract

Abstract Optical bistability (OB) is a phenomenon that describes a light induced phase transition in the non-equilibrium state. It is vital for all-optical computing and communication, serving as the basis for switches, logic gates, transistors, and memory. By enabling two stable light states, OB allows storage and fast switching, making high-speed, energy-efficient data processing possible. In this work we study the phenomenon in a two-band semiconductor in an optical cavity. Starting from a many-body Hamiltonian of optically generated electrons, holes and light-semiconductor interaction and Coulomb electron–electron, hole–hole and electron–hole interactions, we obtain the optical Bloch equations, in the mean field approximation, where relaxation is included phenomenologically. We obtain expressions for particle density, excitonic pair density and output intensity as non-linear functions of input light intensity. All these quantities show bistable behaviour, with two stable phases, and hysteresis in the non-equilibrium state. Equilibrium is ensured by introducing damping terms for the particle density amplitude, excitonic density amplitude, and cavity photon amplitude phenomenologically. The electron–hole pairs increase with light intensity, shows bistable features and then disappears with further increase in the input light intensity. The bistable behaviour becomes pronounced as we pass from low Coulomb interaction strengths to high Coulomb interaction strengths between electrons and holes. For sub-bandgap excitations, the output light versus incident light shows a complex behaviour.

DOI: 10.1088/1402-4896/ae73bd

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Within the framework of a simple numerical model, we investigate the optical properties of a laser-excited direct-band-gap semiconductor (CdS) in the case when both free and bound electron-hole pairs are present. At low temperatures the ionization of excitons proceeds via a first-order phase transition, which is closely related to the Mott transition, and we argue that in direct-band-gap semiconductors it is not suppressed by the electron-hole liquid condensation, as it is in indirect-band-gap materials. The existence of the two corresponding ionization phases with different optical properties is shown to result in optical bistability (OB), which is quite similar to the increasing-absorption (resonatorless) OB but has some peculiarities of its own. Our model also predicts another optical manifestation of this ionization phase transition---the possibility of absorption oscillations at resonant excitation of excitons.

We present a fully-quantum-mechanical theory of the intracavity interaction of coherent light with semiconductors. Interaction is assumed to occur via excitons. Using a master-equation approach we include such effects as exciton-lattice and exciton-exciton interactions. In the two cases of high and low exciton densities, steady-state analysis reveals bistability and hysteresis in the system. Bistability of a dispersive and absorptive nature in both exciton number and output intensity, dependent on input intensity is found. The bistability displayed in the high-density case agrees qualitatively with the experimental curves obtained by Gibbs et al. for GaAs. As yet the low-density bistability has not been experimentally observed.

An electron-hole system in a direct-gap semiconductor that is coherently excited by a high-intensity laser is investigated. The stationary state of the system in the presence of laser field is described by Bogolyubov quasiparticles. Using a mean-field approximation, we derive a set of basic equations including electron-electron, hole-hole, and electron-hole screened Coulomb interactions. The screening effects are incorporated self-consistently on the basis of a quasistatic random-phase approximation. The stationary state has a fixed chemical potential and is controlled by the frequency of the laser field. By numerical analysis of the basic equations, we show that a resonatorless bistability occurs; that is, an electron-hole pair-density bistability with respect to the excitation energy is shown to be caused by many-body effects via the screened Coulomb interaction. We clarify how the stationary state changes its entity depending on the frequency and intensity of the laser field, and how such a characteristic behavior is observed in optical spectra of probe light.

The optical spectra of laser-excited semiconductors change with varying laser intensity. Close to exciton or biexciton resonances these optical nonlinearities are, e.g., large enough to obtain optical bistability. The cause for these large nonlinearities are many-body effects in the system of the electron-hole pair excitation. The use of nonequilibrium Green’s functions, or if a quasi-equilibrium exists of thermal Green’s functions, makes it possible to take radiative and Coulomb interactions consistently into account.

We consider an electron-hole system illuminated by a laser and show that the system shows bistable and multistable behaviours. The mechanisms responsible for these behaviours are discussed in terms of excitonic and phonon interactions. It is found that both the excitonic and the phonon effects contribute to the multistability in the system. With an increase in the strength of the phonon interactions, the system passes from a phase of multistability to a phase of bistability; the reverse happens as the strength of the electron-hole interaction increases.

Optical bistability (OB) can be defined as the existence of two stable states for one set of optical input conditions. It can be seen in many different systems which generally combine some microscopic nonlinearity (e.g., intensity-dependent refractive index) with some macroscopic feedback (e.g., a Fabry-Perot cavity). OB shows not only hysteresis but also switching transitions. By adjusting the degree of feedback various related effects are also possible (e.g., optical limiters, optical transistors, and several kinds of oscillation phenomena).